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Date November 2014 Marks available 3 Reference code 14N.3.SL.TZ0.2
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Determine Question number 2 Adapted from N/A

Question

This question is about standing (stationary) waves.

The diagram shows a tube that is open at both ends.

N14/4/PHYSI/SP3/ENG/TZ0/02_01

Point A shows the position of one air molecule in the tube. A standing sound wave (not shown in the diagram) is set up in the tube.

The graph shows the variation of displacement s with time t for the molecule at point A.

N14/4/PHYSI/SP3/ENG/TZ0/02_02

Outline whether the standing wave is transverse or longitudinal.

[1]
a.

The standing wave in the tube corresponds to the fourth harmonic. The speed of sound in the tube is 340 ms1. Using the graph, determine the length of the tube.

[3]
b.

The tube is now closed at one end and the first harmonic is sounded. Outline why the tube that is open at both ends produces a first harmonic with a wavelength shorter than the first harmonic of the tube that is closed at one end.

[1]
c.

Markscheme

(longitudinal)

the standing wave is formed of (travelling) sound waves (which are longitudinal);

Do not allow responses that focus only on travelling waves.

a.

the frequency is f=11.25×103 (= 800 Hz);

and the wavelength is λ=vf=340800 (=0.425 m);

the fourth harmonic corresponds to 2 wavelengths in the tube, thus L=2λ=0.85 m;

b.

the length of the tube closed at one end corresponds to λ4, while the length for the tube open at both ends corresponds to λ2;

c.

Examiners report

(a) was very badly answered, with few appreciating that the standing wave is made from 2 (or more) travelling sound waves.

a.

(b) was usually well attempted, with arithmetical errors or errors in the relationship between wavelength and pipe length giving any difficulty.

b.

There was a mixed set of responses to (c), from those who clearly understood to those who could not give a mathematical reason.

c.

Syllabus sections

Core » Topic 4: Waves » 4.5 – Standing waves
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